Head on to the new corridor. A short cut-scene will appear on the screen very shortly (#1). Lara will find one of the objects that belonged to her mother. You may proceed to the next section. You will have to use the grapple in order to get to the other side of a huge gap. A second trap has been located nearby. This time you'll have to hurry, because there's a single enemy soldier here (#2). Once you've safely landed, start shooting at him.
You should be able to reach a new part of the complex very soon. Start off by using two of the nearby poles (#1). Thanks to that, you will be able to reach a narrow ledge. You should know exactly what has to be done right now. There's a new pole nearby (#2). Make a jump towards it. After that, head on to the upper platform.
You will probably notice a large group of enemy soldiers in the distance. You might want to consider making their lives a little bit harder. Press the E key in order to kick all of the nearby barrels (#1). These objects will explode in a few seconds. Start running towards the right platform. You will have to deal with the remaining enemy soldiers (#2). I would recommend taking them down from a distance (you will have to use the machine gun).
Once all of the enemy soldiers are gone, turn right. There are THREE ropes here (#1). You will have to use them in order to reach the opposite platform. I guess I don't have to remind you to be EXTREMELY careful. The jumps must be very precise. Once you've reached your destination, turn left and head on to the new tunnel (#2).
Be careful! There's a tiger here (#1)! You should kill it quickly, however it is not necessary, because you won't be returning here anymore. Once you've dealt with his problem, head on to the left stairs. They are destroyed, so you will have to make a jump. Now use the nearby rope (#2). It's very important to make this jump very quickly. Thanks to that, you will avoid getting smashed by a huge ball.
Turn left (you should be still hanging on a rope!). Wait for one of the balls to get past you. Now make a jump towards the stairs. Start moving upwards (#1). There's a small button here (on the floor). You will have to stand on it and wait for the gate to open (#2). Enter the new corridor (you might want to consider making a dive roll move).
Get ready! You will have to deal with the second boss of the game. As you've probably suspected, it's going to be Rutland (#1). Just as before, he's going to be equipped with some additional powers. It'll make this fight a lot more difficult, although there's nothing to be worried about. First of all, you will have to avoid most of its attacks. Rutland will be attacking you from a small distance (#2). It would be wise to make a lot of jumps, so you don't get caught too often. Furthermore, you will have to avoid his grenades. You might not see all of them at first glance.
If you decide to wound the boss, you'll probably notice that he regenerates himself by using one of the mechanisms located on the upper floor. You will have to do something about this. Start off by entering the Accurate Aim mode. You will have to destroy four red objects (#1). It'll probably take you some time. Wait for the boss to regenerate himself again and use the grapple. You will have to pull all four highlighted objects towards Lara (#2). Each action will allow you to destroy a part of the mechanism. Rutland won't be able to use these altars anymore.
Now for the easy part. Rutland won't be able to regenerate anymore, so you might as well start shooting at him (#1). You'll still have to avoid most of his attacks. Thankfully, he won't be alive too long, especially since he's rather weak. Once you've dealt with him, a new cut-scene will appear on the screen (#2). You will also discover some interesting things about Amanda. Apparently she has visited the Croft manor a while ago. This is it for this mission. Lara will decide to visit one of the science laboratories located in Kazakhstan.